Ordering Default Theories and Nonmonotonic Logic Programs

Chiaki Sakama

Theoretical Computer Science, vol.338, pages 127-152, 2005.

Abstract

First-order theories are ordered under logical entailment based on the
amount of information derived from theories.
In default logic, on the other hand,
a theory contains default information as well as definite information.
To order default theories, distinguishing different sorts of information is
necessary to assess the information content of a default theory.
For this purpose, we first introduce a multi-valued interpretation of default
theories using a ten-valued bilattice.
It distinguishes between definite and credulous/skeptical default information
derived from a theory, and is used for ordering default theories
based on their information contents.
We then apply the technique to order nonmonotonic logic programs
under the answer set semantics.
The results of this paper provide a method for comparing default theories
or nonmonotonic logic programs in a manner different from the conventional
extension/model-based viewpoint. Moreover, they
have important application to induction from nonmonotonic theories.